glacial cycles: the 100,000-year problemmcgehee/seminars/climate...glacial cycles (milankovitch...

1

Glacial Cycles: the 100,000-Year Problem

Richard McGehee

http://www.tqnyc.org/NYC052141/beginningpage.html

Seminar on the Mathematics of Climate ChangeSchool of Mathematics

April 13, 2011

Glacial Cycles: the 100,000-Year Problem

Ice-Albedo Feedback

Climate in the Cenozoic Era

Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J. 2 (2008)

Myr

Glacial Cycles

Climate During the Past 4.5 Myr

2.5

3

3 58O)

Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography,20, PA1003, doi:10.1029/2004PA001071.

3.5

4

4.5

5

5.5

‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

Benthic Data (δ18

time (Kyr)

Glacial Cycles

2.5

3

O)

Climate During the Past 1.0 Myr

Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography,20, PA1003, doi:10.1029/2004PA001071.

3.5

4

4.5

5

5.5

‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0

Benthic Data (δ18O

time (Kyr)

Recent (last 400 Kyr) Temperature Cycles

Vostok Ice Core Data

Glacial Cycles

J.R. Petit, et al (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica, Nature 399, 429-436.

2

What Causes Glacial Cycles?

The glacial cycles are driven by the variations in the Earth’s orbit (Mil k it h C l ) i i ti i i i l

Widely Accepted Hypothesis

Glacial Cycles

(Milankovitch Cycles), causing a variation in incoming solar radiation (insolation).

This hypothesis is widely accepted, but also widely regarded as insufficient to explain the observations.

The additional hypothesis is that there are feedback mechanisms that amplify the Milankovitch cycles. What these

feedbacks are and how they work are not fully understood.

Heat Balance

Glacial Cycles

Historical Overview of Climate Change Science, IPCC AR4, p.96http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf

Eccentricity

Glacial Cycles

http://www.crrel.usace.army.mil/permafrosttunnel/Ice_Age_Earth_Orbit.jpg

Obliquity

Glacial Cycles

http://upload.wikimedia.org/wikipedia/commons/6/61/AxialTiltObliquity.png

Precession

Glacial Cycles

http://earthobservatory.nasa.gov/Library/Giants/Milankovitch/milankovitch_2.html

Eccentricity

0.02

0.03

0.04

0.05

0.06

eccentricity

Glacial Cycles

J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, Astronomy & Astrophysics 428, 261–285.

Note periods of about 100 Kyr and 400 Kyr.

0.00

0.01

‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0

time (Kyr)

3

Obliquity

23.0

23.5

24.0

24.5

bliquity (degrees)

Glacial Cycles

Note period of about 41 Kyr.

22.0

22.5

‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0

ob

time (Kyr)


Precession Index

Glacial Cycles

‐0.02

0.00

0.02

0.04

0.06

Note period of about 23 Kyr.

index = e sinρ, where e = eccentricity and ρ = precession angle (measured from spring equinox)

‐0.06

‐0.04

‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0

time (Kyr)


Glacial Cycles

Eccentricity Power Spectrum

Glacial Cycles

Obliquity Power Spectrum

Glacial Cycles

Precession Index Power Spectrum Lisiecki–Raymo δ18O Stack

2.5

3

3.5

4

4.5

5

5.5

18O

Lisiecki Data

Glacial Cycles

‐5000 ‐4000 ‐3000 ‐2000 ‐1000 0

Kyr

0

5

10

15

20

25

30

0 0.01 0.02 0.03 0.04 0.05 0.06

precessionobliquityeccentricity

4

Why obliquity and eccentricity?

Incoming Solar Radiation (Insolation), averaged over the entire globe and over a full year, depends only on eccentricity e , not on

either obliquity or precession.

0

21

QQ e

e

Glacial Cycles

2 2

22

0

2, 1 1 sin cos coss y y y d

,I Q e s y

Insolation as a function of latitude, averaged over a full year, depends on eccentricity e and obliquity β , but not precession.

where

sin latitudey

Why obliquity over eccentricity?

Possible explanation: Ice-albedo feedback

Ice reflects more energy than land or water.

more ice → less energy → colder → more ice

l i l i

Glacial Cycles

less ice → more energy → warmer → less ice

Heat Balance

Glacial Cycles

Historical Overview of Climate Change Science, IPCC AR4, p.96http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf

Budyko-Sellers Model

, : annual mean surface temperatureT T y t

sin latitude y 0 1y

1 ,T

R Qs y y A BT C T Tt

insolation albedo re-radiation transport

Glacial Cycles

1

01s y dy

sin latitude y 0,1y

1

2

, ,, albedo

, .

yy

y

: global annual mean insolationQ

: relative annual mean insolations t

1

0, : global annual mean temperatureT t T y t dy

: ice boundaryy

equilibrium temperature profiles

10

20

30

Two equilibrium solutions:

Solve for equilibrium solution T*(y) .Set right hand side = 0.

Glacial Cycles

-50

-40

-30

-20

-10

0

10

0.0 0.2 0.4 0.6 0.8 1.0

tem

pe

ratu

re (º

C)

sin(latitude)

ice free snowball small cap big cap

small cap: stablelarge cap: unstable

Not equilbria:

ice freesnowball


1 ,T

R Qs y y A BT C T Tt

Note that the equilibrium solution T*(y) depends on Q and s(y) , which depend on the eccentricity e and the obliquity β . Therefore, the equilibrium location η of the ice boundary and

Glacial Cycles

, q η ythe equilibrium global mean temperature (GMT) depend on the

eccentricity and the obliquity.

We can use the computed values of eccentricity and obliquity to compute the ice boundary and GMT over the glacial cycles.

0

21

QQ e

e

2 2

22

0

2, 1 1 sin cos coss y y y d

5


ice boundary

Glacial Cycles

global mean temperature

Model output:

power spectra

Model output:ice boundary

Glacial Cycles

0

5

10

15

20

25

30

0 0.01 0.02 0.03 0.04 0.05 0.06

precessionobliquityeccentricity

Model output:global mean temperature

Climate data

The ice-albedo feedback model correctly predicts the dominance of obliquity, but it fails to explain most of the

other features of the climate data.

2.5

3

3.5

4

thic Data (δ18O)

Climate data

Glacial Cycles

4.5

5

5.5

‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

Bent

time (Kyr)

Model output

2.5

3

3.5

4ata (δ18O)

41 Kyr dominates 100 Kyr dominates

Glacial Cycles

4

4.5

5

5.5

‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

Benthic Da

time (Kyr)

100,000 Year Problem: What’s up with the last million years?Did eccentricity reassert itself? Or something else?

Huyber’s Analysis of Deglaciations

Glacial Cycles

Red dots: deglaciations.

Peter Huybers, "Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression," Quaternary Science

Reviews 26, 37-55 (2007).

Glacial Cycles

The deglaciations are triggered by obliquity cycles, but sometimes they don’t trigger. When cycles are skipped, the

deglaciations can be separated by 80 Kyr or 120 Kyr,

Huyber’s Analysis of Deglaciations

g p y y y ,creating the appearance of 100 Kyr cycles.

6

Huyber’s Triggering Model

1 if

0 if t t t

tt t

t t

V V TV

V T

T at b c

: ice volume at time

: threshold variable

: rate of increase of ice volume

: normalized obliquity

t

t

t

V t

T

Glacial Cycles

Units and constants

t : KyrV : chosen so that η = 1.

θ’: mean zero and variance onea = 0.05b = 126c = 20


Glacial Cycles

black: modelred: data


Glacial Cycles

Huyber’s model produces the decline in temperature and the increase in period and amplitude of the glacial cycles, but it depends heavily on

an unspecified decline in the sensitivity of the triggering mechanism over last two million years.

What about greenhouse gases and the carbon cycle?

Andrew Hogg suggested a model incorporating the carbon cycle.

-2

0

2

4

050100150200250300350400450

kiloyear bp

atu

re

Vostok Core Sample DataPetit, et al, Nature 399 (June 3 1999), pp.429-436

Glacial Cycles

-10

-8

-6

-42

tem

per

a

150

200

250

300

050100150200250300350400450

kiloyear bp

atm

os

CO

2 p

pm

Hogg’s Model

4

0 1 max

,

max ,0 .

dTc S t G C T

dtdC dT

V W W C C Cdt dt

Glacial Cycles

CO2 outgassingweatheringvolcanos

0

2sin

ln

ii i

tS t S S

CG C G A

C

insolation

greenhouse forcing

Andrew McC. Hogg, "Glacial cycles and carbon dioxide: A conceptual model," Geophysical Research Letters 35 (2008).

Glacial Cycles

Hogg’s Model

7

Hogg’s Model

Glacial Cycles

Hogg’s model shows how the carbon cycle can act as a feedback amplifying and modifying the insolation forcing, but the forcing is

somewhat artificial, and the triggering mechanism is difficult to justify. Also, it does not solve the 100,000-year problem.

What if the 100,000 year glacial cycle is not driven by eccentricity, but is a natural oscillation of the Earth’s climate?

Saltzman and Maasch suggested just such a model.

Glacial Cycles

Salzman-Maasch Model

X X Y uM t

global ice mass

Milankovitch forcing

Barry Salzman and Kirk A. Maasch, "A Low-Order Dynamical Model of Global Climatic Variability Over the Full Pleistocene," Journal of Geophysical Research 95 (D2), 1955-1963 (1990)

2 2Y pZ rY sZ Z Y

Z q X Z

atmospheric CO2

deep ocean temperature

Glacial Cycles


unforced


Glacial Cycles

forced

Glacial Cycles

The Salzman-Maasch model shows how the carbon cycle and the ocean currents can interact to produce unforced oscillations with periods of about 100,000 years. The same model with slightly

different parameters can exhibit stationary behavior. By forcing the d l ith Mil k it h l d b l l i th t


model with Milankovitch cycles and by slowly varying the parameters over the last two million years, they can produce a bifurcation from

small oscillations tracking the Milankovitch cycles to large oscillations with a dominant 100,000 year period.

Seems like a nice idea, but it is not widely accepted as the explanation.

Glacial Cycles

The Mathematics and Climate Research Network (MCRN) has a Webinar working group developing a model incorporating ice-albedo

feedback with the carbon cycle.

Local expert: Samantha Oestriecher

Current Project

Local expert: Samantha Oestriecher

8

Glacial Cycles

100 Kyr cycles during the last million years, but 41 Kyr cycles before that.

The 100,000-Year ProblemSummary

Why?

Huybers: Obliquity rules, but glaciers started skipping beats. Alternating 80 Kyr and 120 Kyr looks like 100 Kyr

Saltzman & Maasch: Under some conditions, the climate naturally oscillates at 100 Kyr. Those conditions arose 1 Myr ago. Before that,

the climate tracked Milankovitch.

Other ... ?

glacial cycles: the 100,000-year problemmcgehee/seminars/climate...glacial cycles (milankovitch...

Documents